This additional background material gives a
short account of the discovery and its importance and is written
mainly for physicists.

1. A breakthrough in low temperature
physics
The pioneering work of David Lee, Douglas Osheroff and Robert
Richardson in the beginning of the 1970's at the low-temperature
laboratory of Cornell University has given a most valuable
contribution to our current view of the manifestations of quantum
effects in bulk matter. The anisotropic superfluid helium-3,
appearing below a critical temperature of about two thousandths
of a degree above the absolute zero, is considered to be a
particular kind of Bose-Einstein condensate with a rich set of
physical properties. The study of this exotic quantum liquid has
led to concepts that are of general importance and, e.g., could
become useful for the theoretical treatment of high temperature
superconductors. Recently phase transitions in helium-3 have been
studied as a model for the dynamics of the cosmological phase
transitions that are thought to have occurred a fraction of a
second after the Big Bang (see Nature, July 25, and Science,
August 2, 1996). Critical points of superfluid helium-3 are used
to define temperature scales at values extremely close to the
absolute zero.

2. The discovery
Superfluidity in helium-3 first manifested itself as small
anomalies in the melting curve of solid helium-3, i.e. as small
structures in the diagram representing pressure against time,
when the fluid was cooled. It is always tempting to consider
small deviations as more or less inexplicable peculiarities of
the equipment, but the discoverers became convinced that there
was a real effect. They were actually not looking for
superfluidity, but for an antiferromagnetic phase in solid
helium-3, which according to predictions was to appear below 2
mK. It was thus natural that they, in their first publication
1972, interpreted the effect as the observation of such a phase
transition.

The agreement was not perfect, but by
further development of their technique and new measurements they
could, just a few months later, pinpoint the effect. It actually
turned out to involve two phase transitions in the liquid
phase, at 2.7 and 1.8 mK respectively.

The discovery became the starting point of
an intense activity among low temperature physicists. The
experimental and theoretical developments went hand-in-hand in an
unusally fruitful way. The field was rapidly mapped out, but
fundamental discoveries are still being made.

3. Particle statistics and
superfluidity
In quantum physics the atoms in a gas are described by a
wavefunction which is a function of all the coordinates of the
atoms, but which only specifies the probability of finding a
particle in a given region at a given time. In the quantum regime
(which applies at high density or low temperature) the
indistinguishability of the atoms leads to dramatic quantum
effects. In nature there are two fundamental types of particles,
fermions and bosons. Fermions have half-integral spin and are
described by wavefunctions that are antisymmetric in the exchange
of two particles, i.e. the wavefunctions change sign when two
particles change places, and they follow what is called
Fermi-Dirac statistics. Bosons have integral spin and symmetric
wavefunctions, i.e. their wavefunctions are unchanged when two
particles are exchanged, and they follow Bose-Einstein
statistics. Fermions tend to avoid each other and a gas of
fermions can have at most one particle in each one-particle
quantum state. Bosons, on the other hand, are more sociable and
can occupy the same quantum state. Below a certain temperature,
which depends on the particle density, the bosons tend to gather
in a Bose-Einstein condensate in the quantum state of the lowest
energy and momentum. They are then described by one and the same
wavefunction.

A pure Bose-Einstein condensate of
(bosonic) atoms that only interact weakly was not experimentally
produced until last year. Then a number of groups managed to cool
small samples of dilute gases to temperatures well below one
microkelvin. But a type of Bose-Einstein condensate, with atoms
condensed into the ground state, was identified already in the
1930's, namely the superfluid phase of helium. This quantum
liquid is freely flowing (without viscosity), can penetrate fine
pores that are closed for ordinary liquids and for many gases,
can creep upwards along walls and is an excellent heat
conductor.

Helium mainly consists of the isotope
helium-4, which is a boson (electronic and nuclear spins are
zero). The more rare isotope helium-3, on the other hand, has
nuclear spin 1/2, is a fermion and as such cannot undergo
Bose-Einstein condensation. But in explaining the phenomenon of
superconductivity in metals in 1957, Bardeen, Cooper and
Schrieffer showed that fermions (in this case electrons) under
certain conditions can make up pairs (Cooper pairs) that behave
as bosons. These pairs can then undergo condensation to a ground
state. In principle this explains the 1972 finding of the
phenomenon of superfluidity in helium-3 by Lee, Osheroff and
Richardson. But the nature of the pairing and the properties of
the pairs are very different in the two cases.

In a superconducting metal it is the
surrounding lattice of positive ions that provides the mechanism
making it possible to pair together electrons with opposite
momenta and spin to quasiparticles having zero orbital angular
momentum or spin (L=S=0). In the superfluid phase of helium-3 the
atoms themselves provide the pairing interaction, through
magnetic interaction (the superfluid phase is almost
ferromagnetic), and the pairs are more complicated. The atoms in
the pair rotate around each other and the pair has one unit of
internal orbital angular momentum (L=1). The nuclear spin
magnetic moments tend to be oriented along a common direction
(S=1). The wave function which describes the pair is a complex
valued function and has both amplitude and phase. This means that
the wavefunction of a superfluid helium-3 pair has
2(2L+1)(2S+1)=18 real components, as compared to 2 for the
superconducting electron pair. Even though some components are
coupled to each other (there is a spontaneous breaking of the
symmetry in spin-orbit space) the wave function is still quite
complicated and gives rise to a rich set of orientational
effects.

In the condensate, the bosonic
quasiparticle pairs are coupled to each other and can be
described by a macroscopic wave function with a well defined
phase. This means that the pairs, with their spinning nuclei and
partners rotating around each other, all move coherently so that
their individual nuclear spins and orbital angular momenta are
coupled to a correlated state with large spatial extension. Some
consequences of this are that a minimum energy (gap energy) is
needed to break up the condensate, that the liquid cannot rotate
freely above a critical rotational velocity, but vortices appear
with quantized circulation, and that Josephson effects appear,
e.g., leading to a kind of "ringing" in the liquid after the
variation of a magnetic field over the sample. Most of the
theoretical concepts regarding the paired state and the pairing
mechanism were developed already before the experimental
discovery, by, among others, Anderson and Morel (later on also
with Brinkman), by Vdovin, and by Balian and Werthamer, and
others. Experiments on superfluid helium-3 have later on helped
to discriminate among different theories.

4. The experimental technique
Helium is an inert gas that is present as a small component in
ordinary air (about one part in 200 000). But the fraction of the
isotope helium-3 is about one million times smaller and it would
be too costly to extract it out of air or out of ordinary helium
gas. Instead it can be produced by irradiation of lithium by
neutrons from a nuclear reactor. After the nuclear reaction and
beta decay a gas rich in helium-3 is left, which is sold at a
high price.

Both isotopes of He are inert and light
gases, which among other things means that their electronic
dipole polarizabilities are small, thus making the van der Waals
interaction between individual atoms weak, but also that the zero
point motion is large. This implies that the condensed gas,
liquid helium, does not freeze at ordinary pressure, but remains
in liquid form even at temperatures close to the absolute zero.
In this respect helium is unique among all the elements of the
periodic table. It is only under high pressure at low
temperatures that the liquid helium crystallizes and transforms
into a solid phase.

Several powerful techniques for cooling
were developed during the 1960's. Lee, Osheroff and Richardson
used a method that had been proposed by Pomeranchuk and which was
put into practical use by Anufriev and later developed by, among
others, the scientists at Cornell. The method makes use of the
remarkable property of helium-3 that the liquid phase at low
temperature is more well-ordered than the solid phase. (Ordinary
liquids are much more disordered, have a higher entropy, than the
corresponding crystals, with their periodically ordered rows of
atoms.) By applying a pressure to the liquid, some parts of it
are transformed into the solid phase. These parts thus transform
from a higher to a lower order, for which heat is needed (cf. the
melting of an ordinary crystal). This heat is taken from the
remaining liquid, which thus is cooled further.

Using Pomeranchuk cooling one can reach a
final temperature just below 2 mK before all the liquid has been
transformed into the solid phase. The process is hampered by not
being continuous, but it has several positive properties. The
cooling power is high and the heat contact with the liquid
helium-3 sample is good, since the cooling medium is the same as
the sample. At very low temperatures it can otherwise be
difficult to get a good heat contact; it can easily happen that
the cooling agent, the sample and the thermometer have different
temperatures. Different excitations (e.g., thermal motions among
the atoms, spin waves and electrons) may also not be in thermal
equilibrium.

5. Discovery and properties of
superfluid helium-3
The scientists at Cornell were low temperature specialists and
had built their own apparatus. But in their first measurements on
helium-3 they had a problem with their thermometer at below a few
thousandths of a degree from absolute zero. They decided to
monitor the internal pressure in the sample under an external
pressure that increased uniformly with time. It was the research
student Osheroff who observed a change in the way the internal
pressure varied with time. He did not put the observation aside
as being due to some feature of the apparatus, but instead
insisted that it was a real effect. He observed two anomalies,
shown in Fig. 1. They turned out to be the transition to phase A,
where the individual members of the boson pairs have parallel
spins, and to the phase B, in which they have both parallel and
anti-parallel spins. (In a magnetic field, phase A will increase
at the expense of phase B, as seen in a
pressure-against-temperature diagram. Then also a new phase
(A1) appears, in which the
pairs have atoms with parallel spins (as in phase A) and they all
point in the same direction.)

Another speciality of the group at Cornell
was the nuclear magnetic resonance technique (NMR). In an applied
magnetic field the nuclear spins of the sample atoms will rotate
around the field lines. The frequency of rotation is given by the
strength of the field and by the magnetic moments of the nuclei.
When the frequency becomes equal to that of an applied radio
frequency (r.f.) field, resonance appears and the absorption of
the r.f. field increases. This kind of measurement gives valuable
information on the magnetic state of the helium-3 nuclei. Lee,
Osheroff and Richardson found characteristic changes of the
resonance frequency at the phase transition, changes that are
dependent on the magnetic field strength and on the temperature
and are different in the A and B phases. The theoretician
Leggett could,
within a few weeks, explain the characteristic behaviour in
detail. He showed that in each pair the nuclear spins are coupled
with the rotation, and pointed out the importance of the phase of
the macroscopic wave function that describes the condensate.

The fact that the new phases of helium-3
really were superfluid and could flow without resistance was
shown by two groups soon after the discovery. A group at the
University of Technology in Helsinki, led by Olli Lounasmaa,
measured the damping of a string vibrating in the liquid. They
showed that the damping diminished by a factor of about 1 000 as
the liquid was cooled from above 2 mK to 1 mK. The group led by
the late John Wheatley at La Jolla detected and measured the
velocity of the so-called fourth order sound. This is not a
pressure or density wave, as in ordinary sound, but a temperature
wave at constant pressure appearing in fine pores. A persistent
flow experiment in Helsinki showed that the flow of superfluid
helium-3 in a torus, with packed powder and helium-3 inside, did
not decay, at least on the scale of a few days, in the B phase
(but not in the anisotropic A phase). This implied a viscosity at
least 12 orders of magnitude smaller than the one in the normal
fluid helium-3.

6. Research on superfluid helium-3
today
The most convincing experiments testing the coherence of a
superfluid are probably those showing the appearance of quantized
vortices. When a superfluid is set in rotation and the velocity
of rotation exceeds a critical value, microscopic vortices
appear. The circulation around such a vortex cannot take on any
arbitrary value, but is quantized. This is known from "ordinary"
superfluid helium. In helium-3 the vortices can take on
complicated appearances, in fact eight different types of
vortices have been seen with discontinuous or continuous flow in
the vortex cores. Each of them represents a novel topological
object with peculiar symmetry and structure. NMR, vibrating
strings and other methods have been applied to study the detailed
structure of vortices. Their appearance can even be observed
directly, through an optical fibre and a cooled CCD camera, as
done by the Finnish group which looked on the surface of a
rotating sample.

Another topical field of study is textures,
similar to those appearing in liquid crystals, with nuclear spins
and orbital angular momenta pointing in different directions in
different domains of the liquid. The influence of boundary
surfaces on the orientation of the liquid, the nucleation and
time dependence of phase transitions are also studied.

The phase transitions in helium-3 have
recently been used by two different experimental groups (Grenoble
and Helsinki) in attempts to simulate the formation of cosmic
strings in the early universe. These hypothetical strings might
have appeared as topological defects in the rapid phase
transitions that are thought to have broken the symmetry of the
originally unified interaction and given rise to the four
fundamental forces as we know them today (strong,
electromagnetic, weak, gravitational). Both groups used neutron
induced nuclear reactions to heat their samples locally in such
an abrupt way that the well localised phase transitions were
accompanied by vortex formation, these vortices being the
analogues of the cosmic strings. The validity of a theory
formulated by Zurek, following an idea by Kibble, thus seems to
have been confirmed. The cosmic strings are believed to be of
importance, e.g., for the formation of galaxies.

7. Summary
Superfluidity in helium-3 only appears at very low temperatures,
below about 2 mK, and has found practical applications only for
specialists in the extreme low temperature techniques. Its main
importance has been to develop our understanding of the
complicated behaviour of strongly interacting many-particle
quantum systems, such as quantum liquids, and for the development
of theoretical concepts in the field of macroscopic quantum
phenomena. The understanding of high temperature
superconductivity, which is still not complete, has gained from
concepts developed for helium-3, giving examples of the
interactions that lead to pairing of particles in strongly
interacting systems as well as for the symmetry of the wave
function for such pairs. As a practical application, the
polycritical point, where the superfluid phases A and B are in
equilibrium with the normal liquid phase, is also used as a fixed
point to define temperature scales at very low temperatures.

Special Issue: He3 and
He4, Physics Today, February
1987, including among other articles "Novel magnetic properties
of solid helium-3", by M.C. Cross and D.D. Osheroff, p. 34.

"The 3He Superfluids", by O.V.
Lounasmaa and G.R. Pickett, Scientific American, June 1990.

"The Superfluid Phases of Helium 3", by D.
Vollhardt and P. Wölfle, Taylor and Francis 1990.

Figure 1. Time dependence of the internal pressure in a Pomeranchuk cell containing a mixture of liquid and solid helium-3 under a cycle of uniform compression and decompression. Note the change in slope of the curves at the points A and B and the temperatures at which they appear. The curve is taken from a paper published by D.D. Osheroff, R.C. Richardson, and D.M. Lee in Physical Review Letters 28, 885 (1972), which gives the first description of the new phase transition in helium-3.